It’s normal to assume that there’s an easy way to relate the bandwidth of a power-supply control loop to its transient response—no good reference exists that defines this in simple terms. It seems like a straightforward problem, which should have a simple solution. The higher the bandwidth, the faster the loop responds, and with less voltage deviation.
However, several limiting factors may get in the way of this simple relationship. The first one is the series resistance of the output capacitor. If that resistance is too high, then the load step creates a large voltage deviation before the control loop can respond. Equation 1 gives the peak voltage deviation:
Second, the inductor can cause slew-rate limiting. This is related to the control-loop bandwidth by the voltage across the inductor, calculated with Equation 2:
Third, there’s a critical inductance limit beyond which the duty cycle will saturate. The peak transient voltage is then determined by the large-signal limiting of the inductor current into the output capacitor. This is related to the voltage across the inductor, output capacitor, and series resistance, as expressed by Equation 3:
